PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9751(3^112297-2)/762753576Lelio R Paula03/2012
97523*2^177948-753569Lelio R Paula03/2014
975310^53558+1854353559Patrick De Geest12/2012
975410^53558-2153558Robert Price03/2011
97552^177792-9553521Lelio R Paula02/2011
975613392^9919+9919^1339253521Hans Havermann07/2016
975713105^12132+12132^1310553520Hans Havermann07/2016
975813^48042+8253517Lelio R Paula01/2013
97592^177768+3912153514Yves Minet10/2010
976013835^7366+7366^1383553504Hans Havermann07/2016
976117^43477+8453497Lelio R Paula01/2013
97625*10^53492+953493Dmitry Domanov11/2010
97632^177683+9553488Lelio R Paula01/2011
976411057^13226-13226^1105753482Norbert Schneider12/2017
9765(2^177678+3)/51462753481Lelio R Paula02/2012
97662^177641-25546353476Gary Barnes08/2009
9767p(11608)#/2+1653469Robert Price12/2016
9768(14*10^53465+211)/953466Robert Price11/2017
976937302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
977012001^13104-13104^1200153455Norbert Schneider10/2017
97711829^16384+1828^1638453449Henri Lifchitz01/2007
977210^53442+1262153443Patrick De Geest06/2018
977310^53442-200753442Patrick De Geest06/2018
977435^34608-960253438Enzo Doria03/2013
9775(3^111992+8)/1486753430Lelio R Paula03/2012
97772^177480+186966153427Enzo Doria05/2016
977611791^13122-13122^1179153427Norbert Schneider10/2017
9778(8*10^53411+1)/953411Serge Batalov12/2008
97794*5^76410-353409Lelio R Paula09/2014
97802^177380-11304553397Enzo Doria07/2014
97825^76362-2*3^7636253375Mike Oakes11/2009
978172365!6-2453375Robert Price08/2018
97834159^14747-14053370Enzo Doria07/2012
9784(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9785p(11586)#/2+3253357Robert Price12/2016
978615^45362-4653350Lelio R Paula01/2013
978714147^5892+5892^1414753338Hans Havermann07/2016
97887^63109+4653334Lelio R Paula10/2012
978920^40986-134353325Enzo Doria03/2013
97904*10^53324-8953325Robert Price08/2017
979120^40977-888353313Enzo Doria03/2013
97923^111711+266053300Lelio R Paula10/2012
97932^177040-1186553295Enzo Doria10/2012
9794(7*10^53287+17)/353288Erik Branger03/2014
979535^34506-1075853280Enzo Doria03/2013
9796(11*10^53274-17)/353275Erik Branger03/2014
9797(1017*2^176971-1)/33553275Lelio R Paula03/2015
97985821^14150-14150^582153275Norbert Schneider01/2019
97992^176961-283353271Yves Minet09/2014
98003^111642+11053267Lelio R Paula10/2012
980117^43290-9853267Lelio R Paula01/2013
98027^63028+3653265Lelio R Paula10/2012
9803(22*10^53264+71)/353265Robert Price05/2017
98047^63023-3653261Lelio R Paula10/2012
980519783^492+492^1978353256Anatoly F. Selevich02/2007
980613350^9739+9739^1335053247Hans Havermann10/2015
980714394^4993+4993^1439453235Hans Havermann10/2015
98082^176823-11280753230Enzo Doria06/2014
98091684^16495+16495^168453219Serge Batalov05/2014
981015277^3042+3042^1527753213Hans Havermann06/2016
9811(50322^11317-1)/5032153206Serge Batalov04/2015
98122^176742-159553205Lelio R Paula10/2009
9813(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
981472149!6-1253200Robert Price08/2018
9815(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9816(3*2^176696-1)/29953189Lelio R Paula01/2014
9817(7*10^53185-1)/353186Erik Branger03/2014
98182^176629+46553171Lelio R Paula07/2012
9819(3*2^176604-1)/35953162Lelio R Paula01/2014
982010955^13158-13158^1095553154Norbert Schneider11/2017
98215^76038-1436653149Enzo Doria02/2013
982215156^3209+3209^1515653143Hans Havermann06/2016
98232^176532-283753142Yves Minet09/2014
982452^30967-5153140Norbert Schneider08/2014
98259*5^76023-253139Lelio R Paula09/2014
9826(14283!+1)/46421617753135Michael Porter03/2016
98272^176461-16553121Lelio R Paula02/2011
9828(62*10^53111+1)/953112Serge Batalov05/2010
98292^176403-13953103Lelio R Paula02/2011
983055^30508-253095Lelio R Paula08/2013
9831(48591^11329-1)/4859053090Serge Batalov04/2015
98323^111254-8853082Lelio R Paula10/2012
983315^45129-5653076Lelio R Paula01/2013
9834(640^18913-1)/63953071Eric Chen09/2018
98352^176293-7353070Lelio R Paula01/2011
9837(67*10^53068+41)/953069Robert Price09/2015
983615271^2986+2986^1527153069Hans Havermann06/2016
98382^176255-66753059Yves Minet01/2012
983936471*2^176221+864753053Paul Vanderveen04/2016
9840(19*10^53049-1)/953050Serge Batalov03/2009
98419*2^176203-553044Lelio R Paula03/2014
98422^176205-9439553043Lelio R Paula08/2011
9843(19*2^176224-1)/21791691353042Lelio R Paula01/2014
98448600^13481-13481^860053041Norbert Schneider05/2018
984517^43103+1453037Lelio R Paula01/2013
9846(31*2^176188-1)/355553036Lelio R Paula01/2014
98472^176177+6094753035David Broadhurst05/2002
9848(22*10^53033-7)/353034Erik Branger09/2014
984913810^6909+6909^1381053023Hans Havermann06/2016
98512^176108+1609553014Lelio R Paula10/2009
98502^176107+1891553014Lelio R Paula07/2012
98523^111080-962852999Enzo Doria02/2013
98532^176047-155152996Yves Minet08/2012
98542^176042+7351952994Enzo Doria04/2016
9855lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
98562^175984-11225952977Enzo Doria06/2014
985711^50870+1052976Lelio R Paula01/2013
9858(11*10^52956+19)/352957Robert Price03/2016
98596773^13820-13820^677352942Norbert Schneider11/2018
9860gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9861(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9862(98*10^52931-89)/9952931Ray Chandler11/2010
986313774^6963+6963^1377452931Hans Havermann06/2016
98642^175812-136752925Yves Minet05/2013
98652^175801+1155*17580152922Henri Lifchitz01/2005
986611^50801-909052904Enzo Doria02/2013
98677803^13592-13592^780352904Norbert Schneider07/2018
986843^32374+1252882Robert Price11/2013
9869155^24138+15452871Norbert Schneider12/2018
98702^175628+1352870Lelio R Paula01/2011
98712^175615-174752866Yves Minet09/2012
9872(13*10^52861+107)/352862Robert Price11/2017
98739*2^175586-752858Lelio R Paula03/2014
987412174^12937+12937^1217452854Norbert Schneider04/2016
9875(15*2^175565+1)/835952848Lelio R Paula07/2012
9876(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
987714256^5077+5077^1425652828Hans Havermann06/2016
98782^175467+8287552821Lelio R Paula07/2012
9879(7*10^52819+167)/352820Robert Kinser10/2017
9881(67607*2^175426+1)/352813Lelio R Paula05/2014
988071671!6-3252813Robert Price08/2018
988213^47400-6052801Lelio R Paula01/2013
98834*10^52792+6352793Robert Price06/2016
9885(78557*2^175360+1)/308752791Lelio R Paula06/2014
988418^42055-292952791Enzo Doria03/2013
98869*5^75521+252788Lelio R Paula09/2014
98876^67814+3152770Lelio R Paula10/2012
988870^28600+6952770Norbert Schneider10/2012
988914^46038+9752766Lelio R Paula01/2013
9890(61*10^52763-7)/952764Serge Batalov02/2009
98912*5^75474+952755Lelio R Paula09/2014
989210^52753+282643060952754Robert Price05/2015
989310^52753+18399752754Patrick De Geest01/2016
989410^52753-5015352753Patrick De Geest03/2016
989519846^455+455^1984652751Anatoly F. Selevich02/2007
98962^175217+7297752746Enzo Doria04/2016
9897p(11466)#/2-25652746Robert Price05/2017
9898(4*10^52740+41)/952740Robert Price11/2014
98992^175189+538552738Lelio R Paula08/2009
99002^175160+938552729Lelio R Paula07/2008
990112356^12885+12885^1235652724Norbert Schneider03/2016
99022^175137+1152722Lelio R Paula01/2011
990365^29077-64^2907752715Robert Price08/2013
99042*10^52713-8752714Robert Price06/2016
99052^175106-46552713Lelio R Paula08/2009
99062^175089-5869552708Lelio R Paula08/2009
99082^175045+19552694Lelio R Paula02/2011
9907195^23010-252694Lelio R Paula10/2017
99092^175025+14952688Lelio R Paula02/2011
9910(19^41201+1)/2052685Paul Bourdelais03/2010
9911(436*10^52683-13)/952685Robert Price10/2017
99122*12^48815-5^4881552681Mike Oakes10/2010
9913335^20862-20862^33552678Norbert Schneider09/2015
99142^174983-760552676Lelio R Paula07/2009
99154*10^52667+1952668Robert Price04/2016
9916(10^52667+77)/352667Robert Price01/2017
991711434^12977+12977^1143452664Norbert Schneider04/2016
99182^174941-120352663Lelio R Paula07/2009
99198501^13400-13400^850152655Norbert Schneider03/2018
99202^174910+1270552654Lelio R Paula07/2012
99213^110338+7452645Lelio R Paula10/2012
99225^75303+1252635Lelio R Paula10/2012
99232^174836+25525552631Lelio R Paula07/2009
9924(66^28921+1)/6752622Paul Bourdelais08/2017
992520^40443+952618Lelio R Paula01/2013
9926(11*2^174788+1)/952617Lelio R Paula01/2012
9927(11*2^174786-1)/70352615Lelio R Paula01/2014
992811^50520-129052612Enzo Doria11/2012
9929(670^18617-1)/66952611Eric Chen09/2018
9930(10^52608-19)/952608Robert Price10/2017
9931(9913*2^174736-1)/33352603Lelio R Paula03/2015
993213145^10024+10024^1314552594Hans Havermann05/2016
99335003^14217-15052592Enzo Doria07/2012
99342^174698-405552590Yves Minet02/2018
993519^41123+1052587Lelio R Paula01/2013
99362^174683+1290952585Lelio R Paula01/2011
99372^174643+5952573Lelio R Paula01/2011
9938(1017*2^174640-1)/77352572Lelio R Paula03/2015
993913529^7662+7662^1352952552Hans Havermann06/2016
9940121421#+18876752548Makoto Morimoto02/2016
994120^40375-592352530Enzo Doria03/2013
9942(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9943(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
99442^174462+34552519Lelio R Paula07/2009
9945t(178863)52509Robert Price10/2014
99462^174416+85552505Lelio R Paula07/2009
99476^67467-10352500Lelio R Paula10/2012
9948(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
99497888^13467-13467^788852481Norbert Schneider05/2018
99502^174329-1126552479Enzo Doria06/2014
99512^174314-124152474Yves Minet05/2009
995252^30577-5152471Norbert Schneider08/2014
99539403^13206-13206^940352471Norbert Schneider12/2017
995415692^2205+2205^1569252465Hans Havermann06/2016
9955(2^174281-7)/62881702961552453Lelio R Paula02/2012
9956(2^174240+5)/352451Lelio R Paula02/2012
9957(86*10^52450-221)/952451Robert Price06/2017
9958(62*10^52448-197)/952449Robert Price10/2017
9959(15*2^174221+1)/40352445Lelio R Paula07/2012
996026313!2-3252443Robert Price10/2015
9961(3*2^174214-1)/374872952438Lelio R Paula01/2014
99622*3^109900-552436Lelio R Paula03/2014
99644159^14488-15052432Enzo Doria07/2012
9963(89*10^52431-71)/952432Robert Price11/2015
99652^174170-394152431Yves Minet04/2017
9966(7*2^174171-1)/68552429Lelio R Paula01/2014
99675375^14052-14052^537552420Norbert Schneider10/2018
9968(260137^9679+1)/26013852409Faysal YAtim03/2008
99692^174098+7952409Lelio R Paula01/2011
997035^33940-221452406Enzo Doria03/2013
997115^44557+252404Ray Chandler07/2011
99722^174049-43952394Yves Minet01/2012
99736^67329+11552393Lelio R Paula10/2012
99752^174041+26214552392Lelio R Paula07/2009
9974141^24377+252392Lelio R Paula05/2013
9976lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
99772^174001-595552380Lelio R Paula07/2009
9978lucasV(-1,2,347969)52375Mike Oakes02/2017
99793^109764-14052371Lelio R Paula10/2012
99812*3^109761+752370Lelio R Paula03/2014
99809863^13112-13112^986352370Norbert Schneider10/2017
9983(145^24229+1)/14652366Richard Fischer02/2018
99828094^13399-13399^809452366Norbert Schneider03/2018
99842^173944-11225352363Enzo Doria06/2014
99862^173940+111152362Lelio R Paula01/2011
9985(3126^14983-1)/312552362Richard Fischer03/2015
998715214^2763+2763^1521452358Hans Havermann05/2016
998813200^9247+9247^1320052352Hans Havermann05/2016
9989(1017*2^173867-1)/717552339Lelio R Paula03/2015
999013732^6465+6465^1373252327Hans Havermann05/2016
9991(2^173867-1)/5253663750268952326Donovan Johnson06/2005
99922^173811-68487752323Paul Bourdelais11/2012
99932^173807-595552322Lelio R Paula06/2009
99942^173796-104468952318Paul Bourdelais11/2012
999510^52317+6449752318Patrick De Geest12/2012
999610^52317+6474352318Patrick De Geest12/2012
999810^52317-7152317Robert Price05/2011
999710821^12968+12968^1082152317Norbert Schneider04/2016
9999(298*10^52308-7)/352310Robert Price06/2017
10000(2^173778-3)/5795952308Lelio R Paula02/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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